Are coral reefs growing from the depths of the oceans? ... [The] reply is a simple negative; and a single fact establishes its truth. The reef-forming coral zoophytes, as has been shown, cannot grow at greater depths than 100 or 120 feet; and therefore in seas deeper than this, the formation or growth of reefs over the bottom is impossible.

Ath. There still remain three studies suitable for freemen. Calculation in arithmetic is one of them; the measurement of length, surface, and depth is the second; and the third has to do with the revolutions of the stars in reference to one another … there is in them something that is necessary and cannot be set aside, … if I am not mistaken, [something of] divine necessity; for as to the human necessities of which men often speak when they talk in this manner, nothing can be more ridiculous than such an application of the words.Cle. And what necessities of knowledge are there, Stranger, which are divine and not human?Ath. I conceive them to be those of which he who has no use nor any knowledge at all cannot be a god, or demi-god, or hero to mankind, or able to take any serious thought or charge of them.

Homo hominem arreptum a tellure, et utcunque exigua impulsum vi, vel uno etiam oris flatu impetitum, ab hominum omnium commercio in infinitum expelleret, nunquam per totam aeternitatem rediturum.Were it not for gravity one man might hurl another by a puff of his breath into the depths of space, beyond recall for all eternity.

A hot topic of late, expressed most notably in Bernie Siegel’s best-selling books, has emphasized the role of positive attitude in combating such serious diseases as cancer. From the depths of my skeptical and rationalist soul, I ask the Lord to protect me from California touchie-feeliedom.

A person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings, and aspirations to which he clings because of their superpersonal value. It seems to me that what is important is the force of this superpersonal content and the depth of the conviction concerning its overpowering meaningfulness, regardless of whether any attempt is made to unite this content with a divine Being, for otherwise it would not be possible to count Buddha and Spinoza as religious personalities. Accordingly, a religious person is devout in the sense that he has no doubt of the significance and loftiness of those superpersonal objects and goals which neither require nor are capable of rational foundation. They exist with the same necessity and matter-of-factness as he himself. In this sense religion is the age-old endeavor of mankind to become clearly and completely conscious of these values and goals and constantly to strengthen and extend their effect. If one conceives of religion and science according to these definitions then a conflict between them appears impossible. For science can only ascertain what is, but not what should be, and outside of its domain value judgments of all kinds remain necessary.

After a duration of a thousand years, the power of astrology broke down when, with Copernicus, Kepler, and Galileo, the progress of astronomy overthrew the false hypothesis upon which the entire structure rested, namely the geocentric system of the universe. The fact that the earth revolves in space intervened to upset the complicated play of planetary influences, and the silent stars, related to the unfathomable depths of the sky, no longer made their prophetic voices audible to mankind. Celestial mechanics and spectrum analysis finally robbed them of their mysterious prestige.

All the different classes of beings which taken together make up the universe are, in the ideas of God who knows distinctly their essential gradations, only so many ordinates of a single curve so closely united that it would be impossible to place others between any two of them, since that would imply disorder and imperfection. Thus men are linked with the animals, these with the plants and these with the fossils which in turn merge with those bodies which our senses and our imagination represent to us as absolutely inanimate. And, since the law of continuity requires that when the essential attributes of one being approximate those of another all the properties of the one must likewise gradually approximate those of the other, it is necessary that all the orders of natural beings form but a single chain, in which the various classes, like so many rings, are so closely linked one to another that it is impossible for the senses or the imagination to determine precisely the point at which one ends and the next begins?all the species which, so to say, lie near the borderlands being equivocal, at endowed with characters which might equally well be assigned to either of the neighboring species. Thus there is nothing monstrous in the existence zoophytes, or plant-animals, as Budaeus calls them; on the contrary, it is wholly in keeping with the order of nature that they should exist. And so great is the force of the principle of continuity, to my thinking, that not only should I not be surprised to hear that such beings had been discovered?creatures which in some of their properties, such as nutrition or reproduction, might pass equally well for animals or for plants, and which thus overturn the current laws based upon the supposition of a perfect and absolute separation of the different orders of coexistent beings which fill the universe;?not only, I say, should I not be surprised to hear that they had been discovered, but, in fact, I am convinced that there must be such creatures, and that natural history will perhaps some day become acquainted with them, when it has further studied that infinity of living things whose small size conceals them for ordinary observation and which are hidden in the bowels of the earth and the depth of the sea.

An underwater-listening device, the “hydrophone,” has, in recent years, shown that sea creatures click, grunt, snap, moan, and, in general, make the ocean depths as maddeningly noisy as ever the land is.

As an Art, Mathematics has its own standard of beauty and elegance which can vie with the more decorative arts. In this it is diametrically opposed to a Baroque art which relies on a wealth of ornamental additions. Bereft of superfluous addenda, Mathematics may appear, on first acquaintance, austere and severe. But longer contemplation reveals the classic attributes of simplicity relative to its significance and depth of meaning.

As our technology evolves, we will have the capacity to reach new, ever-increasing depths. The question is: What kind of technology, in the end, do we want to deploy in the far reaches of the ocean? Tools of science, ecology and documentation, or the destructive tools of heavy industry? Some parts of our oceans, like the rich and mysterious recesses of our Atlantic submarine canyons and seamounts, are so stunning and sensitive they deserve to be protected from destructive activities.

Ask a follower of Bacon what [science] the new philosophy, as it was called in the time of Charles the Second, has effected for mankind, and his answer is ready; “It has lengthened life; it has mitigated pain; it has extinguished diseases; it has increased the fertility of the soil; it has given new securities to the mariner; it has furnished new arms to the warrior; it has spanned great rivers and estuaries with bridges of form unknown to our fathers; it has guided the thunderbolt innocuously from heaven to earth; it has lighted up the night with the splendour of the day; it has extended the range of the human vision; it has multiplied the power of the human muscles; it has accelerated motion; it has annihilated distance; it has facilitated intercourse, correspondence, all friendly offices, all dispatch of business; it has enabled man to descend to the depths of the sea, to soar into the air, to penetrate securely into the noxious recesses of the earth, to traverse the land in cars which whirl along without horses, to cross the ocean in ships which run ten knots an hour against the wind. These are but a part of its fruits, and of its first-fruits; for it is a philosophy which never rests, which has never attained, which is never perfect. Its law is progress. A point which yesterday was invisible is its goal to-day, and will be its starting-point to-morrow.”

At quite uncertain times and places,The atoms left their heavenly path,And by fortuitous embraces,Engendered all that being hath.And though they seem to cling together,And form 'associations' here,Yet, soon or late, they burst their tether,And through the depths of space career.

Consider the hateful brew compounded with gleaming, deadly white lead whose fresh colour is like milk…. Over the victim’s jaws and in the grooves of the gums is plastered an astringent froth, and the furrow of the tongue turns rough on either side, and the depth of the throat grows somewhat dry, and from the pernicious venom follows a dry retching and hawking, for this affliction is severe; meanwhile his spirit sickens and he is worn out with mortal suffering. His body too grows chill, while sometimes his eyes behold strange illusions or else he drowses; nor can he bestir his limbs as heretofore, and he succumbs to the overmastering fatigue.

Descriptive geometry has two objects: the first is to establish methods to represent on drawing paper which has only two dimensions,—namely, length and width,—all solids of nature which have three dimensions,—length, width, and depth,—provided, however, that these solids are capable of rigorous definition.The second object is to furnish means to recognize accordingly an exact description of the forms of solids and to derive thereby all truths which result from their forms and their respective positions.

During the time of the Deluge, whilst the Water was out upon, and covered the Terrestrial Globe, … all Fossils whatever that had before obtained any Solidity, were totally dissolved, and their constituent Corpuscles all disjoyned, their Cohesion perfectly ceasing … [A]nd, to be short, all Bodies whatsoever that were either upon the Earth, or that constituted the Mass of it, if not quite down to the Abyss, yet at least to the greatest depth we ever dig: I say all these were assumed up promiscuously into the Water, and sustained in it, in such a manner that the Water, and Bodies in it, together made up one common confused Mass. That at length all the Mass that was thus borne up in the Water, was again precipitated and subsided towards the bottom. That this subsidence happened generally, and as near as possibly could be expected in so great a Confusion, according to the laws of Gravity.

Every new theory as it arises believes in the flush of youth that it has the long sought goal; it sees no limits to its applicability, and believes that at last it is the fortunate theory to achieve the 'right' answer. This was true of electron theory—perhaps some readers will remember a book called The Electrical Theory of the Universe by de Tunzelman. It is true of general relativity theory with its belief that we can formulate a mathematical scheme that will extrapolate to all past and future time and the unfathomed depths of space. It has been true of wave mechanics, with its first enthusiastic claim a brief ten years ago that no problem had successfully resisted its attack provided the attack was properly made, and now the disillusionment of age when confronted by the problems of the proton and the neutron. When will we learn that logic, mathematics, physical theory, are all only inventions for formulating in compact and manageable form what we already know, like all inventions do not achieve complete success in accomplishing what they were designed to do, much less complete success in fields beyond the scope of the original design, and that our only justification for hoping to penetrate at all into the unknown with these inventions is our past experience that sometimes we have been fortunate enough to be able to push on a short distance by acquired momentum.

For a billion years the patient earth amassed documents and inscribed them with signs and pictures which lay unnoticed and unused. Today, at last, they are waking up, because man has come to rouse them. Stones have begun to speak, because an ear is there to hear them. Layers become history and, released from the enchanted sleep of eternity, life's motley, never-ending dance rises out of the black depths of the past into the light of the present.

For me, a rocket is only a means--only a method of reaching the depths of space—and not an end in itself… There’s no doubt that it’s very important to have rocket ships since they will help mankind to settle elsewhere in the universe. But what I’m working for is this resettling… The whole idea is to move away from the Earth to settlements in space.

Half a century ago Oswald (1910) distinguished classicists and romanticists among the scientific investigators: the former being inclined to design schemes and to use consistently the deductions from working hypotheses; the latter being more fit for intuitive discoveries of functional relations between phenomena and therefore more able to open up new fields of study. Examples of both character types are Werner and Hutton. Werner was a real classicist. At the end of the eighteenth century he postulated the theory of “neptunism,” according to which all rocks including granites, were deposited in primeval seas. It was an artificial scheme, but, as a classification system, it worked quite satisfactorily at the time. Hutton, his contemporary and opponent, was more a romanticist. His concept of “plutonism” supposed continually recurrent circuits of matter, which like gigantic paddle wheels raise material from various depths of the earth and carry it off again. This is a very flexible system which opens the mind to accept the possible occurrence in the course of time of a great variety of interrelated plutonic and tectonic processes.

He who would know what geometry is, must venture boldly into its depths and learn to think and feel as a geometer. I believe that it is impossible to do this, and to study geometry as it admits of being studied and am conscious it can be taught, without finding the reason invigorated, the invention quickened, the sentiment of the orderly and beautiful awakened and enhanced, and reverence for truth, the foundation of all integrity of character, converted into a fixed principle of the mental and moral constitution, according to the old and expressive adage “abeunt studia in mores”.

How many famous men be there in this our age, which make scruple to condemne these old witches, thinking it to bee nothing but a melancholike humour which corrupteth thei imagination, and filleth them with all these vaines toyes. I will not cast my selfe any further into the depth of this question, the matter craveth a man of more leisure.Describing melancholy as the innocent affliction of those regarded as witches instead of Satanic influence, while distancing himself from the controversy.

Discours de la conservation de la veue; des maladies mélancholiques, des catarrhes, et de la vieillese (1594). In Richard Surphlet (trans.) A Discourse of the Preservation of the Sight: of Melancholike Diseases; of Rheumes, and of Old Age (1599), 98-9. Quoted in Michael Heyd, Be sober and Reasonable (), 58.

I believe that the useful methods of mathematics are easily to be learned by quite young persons, just as languages are easily learned in youth. What a wondrous philosophy and history underlie the use of almost every word in every language—yet the child learns to use the word unconsciously. No doubt when such a word was first invented it was studied over and lectured upon, just as one might lecture now upon the idea of a rate, or the use of Cartesian co-ordinates, and we may depend upon it that children of the future will use the idea of the calculus, and use squared paper as readily as they now cipher. … When Egyptian and Chaldean philosophers spent years in difficult calculations, which would now be thought easy by young children, doubtless they had the same notions of the depth of their knowledge that Sir William Thomson might now have of his. How is it, then, that Thomson gained his immense knowledge in the time taken by a Chaldean philosopher to acquire a simple knowledge of arithmetic? The reason is plain. Thomson, when a child, was taught in a few years more than all that was known three thousand years ago of the properties of numbers. When it is found essential to a boy’s future that machinery should be given to his brain, it is given to him; he is taught to use it, and his bright memory makes the use of it a second nature to him; but it is not till after-life that he makes a close investigation of what there actually is in his brain which has enabled him to do so much. It is taken because the child has much faith. In after years he will accept nothing without careful consideration. The machinery given to the brain of children is getting more and more complicated as time goes on; but there is really no reason why it should not be taken in as early, and used as readily, as were the axioms of childish education in ancient Chaldea.

I did enjoy the [CCNY geology] field trips. We went upstate and clambered over formations of synclines and anticlines. We had to diagram them, and figure out their mirror images. If you had an anticline here, you should be able to predict a complementing syncline bulging out somewhere else. Very satisfying when I got it right. Geology allowed me to display my brilliance to my non-college friends. “You know, the Hudson really isn't a river.” “What are you talking about? … Everybody knows the Hudson River's a river.” I would explain that the Hudson was a “drowned” river, up to about Poughkeepsie. The Ice Age had depressed the riverbed to a depth that allowed the Atlantic Ocean to flood inland. Consequently, the lower Hudson was really a saltwater estuary.[Powell graduated with a B.S. degree in Geology.]

I had a feeling once about Mathematics—that I saw it all. Depth beyond depth was revealed to me—the Byss and Abyss. I saw—as one might see the transit of Venus or even the Lord Mayor’s Show—a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go.

I had gone on a walk on a fine Sabbath afternoon. I had entered the Green [of Glasgow] by the gate at the foot of Charlotte Street—had passed the old washing-house. I was thinking upon the engine at the time, and had gone as far as the herd's house, when the idea came into my mind that as steam was an elastic body it would rush into a vacuum, and if a communication were made between the cylinder and an exhausted vessel it would rush into it, and might be there condensed without cooling the cylinder. I then saw that I must get rid of the condensed steam and injection water if I used a jet, as in Newcomen's engine. Two ways of doing this occurred to me. First, the water might be run off by a descending pipe, if an outlet could be got at the depth of 35 or 36 feet, and any air might be extracted by a small pump. The second was to make the pump large enough to extract both water and air. ... I had not walked further than the Golf-house when the whole thing was arranged in my mind.[In Robert Hart's words, a recollection of the description of Watt's moment of inspiration, in May 1765, for improving Thomas Newcomen's steam engine.]

In Robert Hart, 'Reminiscences of James Watt' (read 2 Nov 1857), Transactions of the Glasgow Archaeological Society (1859), Vol. 1, 1. Note that these are not the verbatim words of James Watt, but are only a recollection of them by Robert Hart, who is quoting as best he can from memory of a conversation he and his brother had with James Watt that took place over 43 years previously. In his Reminiscences, Hart explains, “I have accordingly thrown together the following brief narrative:— As these meetings took place forty-three years since, many observations that were made at the time may have escaped me at present; yet, when the same subjects are touched on, I have as distinct recollection of his treatment of them as if it were yesterday.”

I had rather believe all the Fables in the Legend, and the Talmud, and the Alcoran, then that this universall Frame, is without a Minde. And therefore, God never wrought Miracle, to convince Atheisme, because his Ordinary Works Convince it. It is true, that a little Philosophy inclineth Mans Minde to Atheisme; But depth in Philosophy, bringeth Mens Mindes about to Religion.

I have seen the sea lashed into fury and tossed into spray, and its grandeur moves the soul of the dullest man; but I remember that it is not the billows, but the calm level of the sea from which all heights and depths are measured.

Speech (5 Jun 1880) at the 7th Republican National Convention, Chicago to nominate John Sherman to be President. In John Tweedy, A History of the Republican National Conventions from 1856 to 1908 (1910), 191. The Convention subsequently nominated Garfield to run for President. He won the election, and was inaugurated on 4 Mar 1881.

If a man has a tent made of linen of which the apertures have all been stopped up, and be it twelve bracchia across (over twenty-five feet) and twelve in depth, he will be able to throw himself down from any height without sustaining injury. [His concept of the parachute.]

In Isaac Asimov and Jason A. Shulman, Isaac Asimov’s Book of Science and Nature Quotations (1988), 3-4, which notes twelve bracchia is over 25 feet. There are other translations with different units. Da Vinci’s illustration in his notebook showed a pyramid-shaped parachute below which hung a man suspended by a few short cords.

If in physics there’s something you don’t understand, you can always hide behind the uncharted depths of nature. You can always blame God. You didn’t make it so complex yourself. But if your program doesn’t work, there is no one to hide behind. You cannot hide behind an obstinate nature. If it doesn’t work, you’ve messed up.

In 1946 [we visited] a rock called Le Veyron, around which sea life swarmed … an undersea paradise.… About thirty years later I returned … to the same depth, to the same caves, at the same time of year. The grotto was empty. Not one single fish lived among the rocks. The verdant gardens were gone.…When I saw Le Veyron, I believed that the sea’s most monstrous force doesn’t live in Loch Ness. It lives in us.

In Man the brain presents an ascensive step in development, higher and more strongly marked than that by which the preceding subclass was distinguished from the one below it. Not only do the cerebral hemispheres overlap the olfactory lobes and cerebellum, but they extend in advance of the one, and further back than the other. Their posterior development is so marked, that anatomists have assigned to that part the character of a third lobe; it is peculiar to the genus Homo, and equally peculiar is the 'posterior horn of the lateral ventricle,' and the 'hippocampus minor,' which characterize the hind lobe of each hemisphere. The superficial grey matter of the cerebrum, through the number and depth of the convolutions, attains its maximum of extent in Man. Peculiar mental powers are associated with this highest form of brain, and their consequences wonderfully illustrate the value of the cerebral character; according to my estimate of which, I am led to regard the genus Homo, as not merely a representative of a distinct order, but of a distinct subclass of the Mammalia, for which I propose a name of 'ARCHENCEPHALA.'

In-depth studies have an influence on general ideas, whereas theories, in turn, in order to maintain themselves, push their spectators to search for new evidence. The mind’s activity that is maintained by the debates about these works, is probably the source of the greatest joys given to man to experience on Earth.

It is to them [fossils] alone that we owe the commencement of even a Theory of the Earth ... By them we are enabled to ascertain, with the utmost certainty, that our earth has not always been covered over by the same external crust, because we are thoroughly assured that the organized bodies to which these fossil remains belong must have lived upon the surface before they came to be buried, as they now are, at a great depth.

It must be conceded that a theory has an important advantage if its basic concepts and fundamental hypotheses are 'close to experience,' and greater confidence in such a theory is certainly justified. There is less danger of going completely astray, particularly since it takes so much less time and effort to disprove such theories by experience. Yet more and more, as the depth of our knowledge increases, we must give up this advantage in our quest for logical simplicity in the foundations of physical theory...

It was cold. Space, the air we breathed, the yellow rocks, were deadly cold. There was something ultimate, passionless, and eternal in this cold. It came to us as a single constant note from the depths of space. We stood on the very boundary of life and death.

Its [mathematical analysis] chief attribute is clearness; it has no means for expressing confused ideas. It compares the most diverse phenomena and discovers the secret analogies which unite them. If matter escapes us, as that of air and light because of its extreme tenuity, if bodies are placed far from us in the immensity of space, if man wishes to know the aspect of the heavens at successive periods separated by many centuries, if gravity and heat act in the interior of the solid earth at depths which will forever be inaccessible, mathematical analysis is still able to trace the laws of these phenomena. It renders them present and measurable, and appears to be the faculty of the human mind destined to supplement the brevity of life and the imperfection of the senses, and what is even more remarkable, it follows the same course in the study of all phenomena; it explains them in the same language, as if in witness to the unity and simplicity of the plan of the universe, and to make more manifest the unchangeable order which presides over all natural causes.

Just as, in civil History, one consults title-deeds, one studies coins, one deciphers ancient inscriptions, in order to determine the epochs of human revolutions and to fix the dates of moral [i.e. human] events; so, in Natural History, one must excavate the archives of the world, recover ancient monuments from the depths of the earth, collect their remains, and assemble in one body of proofs all the evidence of physical changes that enable us to reach back to the different ages of Nature. This, then, is the order of the times indicated by facts and monuments: these are six epochs in the succession of the first ages of Nature; six spaces of duration, the limits of which although indeterminate are not less real; for these epochs are not like those of civil History ... that we can count and measure exactly; nevertheless we can compare them with each other and estimate their relative duration.

Learn to reverence night and to put away the vulgar fear of it, for, with the banishment of night from the experience of man, there vanishes as well a religious emotion, a poetic mood, which gives depth to the adventure of humanity. By day, space is one with the earth and with man - it is his sun that is shining, his clouds that are floating past; at night, space is his no more. When the great earth, abandoning day, rolls up the deeps of the heavens and the universe, a new door opens for the human spirit, and there are few so clownish that some awareness of the mystery of being does not touch them as they gaze. For a moment of night we have a glimpse of ourselves and of our world islanded in its stream of stars - pilgrims of mortality, voyaging between horizons across eternal seas of space and time. Fugitive though the instant be, the spirit of man is, during it, ennobled by a genuine moment of emotional dignity, and poetry makes its own both the human spirit and experience.

Let both sides seek to invoke the wonders of science instead of its terrors. Together let us explore the stars, conquer the deserts, eradicate disease, tap the ocean depths, and encourage the arts and commerce.

Let the mind rise from victory to victory over surrounding nature, let it but conquer for human life and activity not only the surface of the earth but also all that lies between the depth of the sea and the outer limits of the atmosphere; let it command for its service prodigious energy to flow from one part of the universe to the other, let it annihilate space for the transference of its thoughts.

Life, therefore, has been often disturbed on this earth by terrible events—calamities which, at their commencement, have perhaps moved and overturned to a great depth the entire outer crust of the globe, but which, since these first commotions, have uniformly acted at a less depth and less generally. Numberless living beings have been the victims of these catastrophes; some have been destroyed by sudden inundations, others have been laid dry in consequence of the bottom of the seas being instantaneously elevated. Their races even have become extinct, and have left no memorial of them except some small fragments which the naturalist can scarcely recognise.

Literature has her quacks no less than medicine, and they are divided into two classes; those who have erudition without genius, and those who have volubility, without depth; we shall get second-hand sense from the one, and original nonsense from the other.

Mathematics … engages, it fructifies, it quickens, compels attention, is as circumspect as inventive, induces courage and self-confidence as well as modesty and submission to truth. It yields the essence and kernel of all things, is brief in form and overflows with its wealth of content. It discloses the depth and breadth of the law and spiritual element behind the surface of phenomena; it impels from point to point and carries within itself the incentive toward progress; it stimulates the artistic perception, good taste in judgment and execution, as well as the scientific comprehension of things.

My view, the skeptical one, holds that we may be as far away from an understanding of elementary particles as Newton's successors were from quantum mechanics. Like them, we have two tremendous tasks ahead of us. One is to study and explore the mathematics of the existing theories. The existing quantum field-theories may or may not be correct, but they certainly conceal mathematical depths which will take the genius of an Euler or a Hamilton to plumb. Our second task is to press on with the exploration of the wide range of physical phenomena of which the existing theories take no account. This means pressing on with experiments in the fashionable area of particle physics. Outstanding among the areas of physics which have been left out of recent theories of elementary particles are gravitation and cosmology

Nature, everywhere the most amazingly and outstandingly remarkable producer of living bodies, being most carefully arranged according to physical, mechanical, and chemical laws, does not give even the smallest hint of its extraordinary and tireless workings and quite clearly points to its work as being alone worthy of a benign and omnipotent God; and it carries this bright quality in all of its traces, in that, just as all of its general mechanisms rejoice, so also do all of their various smallest component parts rejoice in the depth of wisdom, in the height of perfection, and in the lofty arrangement of forms and qualities, which lie far beyond every investigation of the human mind.

In Pensées (1670), Section 1, No. 28. As paraphrased in W.H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms (1966). From the more complete translation, “Symmetry is what we see at a glance; based on the fact that there is no reason for any difference, and based also on the face of man; whence it happens that symmetry is only wanted in breadth, not in height or depth,” in Blaise Pascal and W.F. Trotter (trans.), 'Thoughts', collected in Charles W. Eliot (ed.), The Harvard Classics (1910), Vol. 48, 15. From the French, “Symétrie, en ce qu’on voit d’une vue, fondée sur ce qu’il n’y a pas de raison de faire autrement: et fondée aussi sur la figure de l’homme, d’où il arrive qu’on ne veut la symétrie qu’en largeur, non en hauteur ni profondeur,” in Blaise Pascal and Léon Brunschvicg (ed.), Pensées de Blaise Pascal (1904), Vol. 1, 37-38.

People have noted with admiration how the progress of scientific enquiry is like the growth of a coral reef; each generation of little toilers building a sure foundation on which their successors may build yet further. The simile is apt in many ways, and in one way in particular that is worth considering. When we see how industrious and how prolific are the coral insects, our chief astonishment should be, not how vast are the structures they have built, but how few and scattered. Why is not every coast lined with coral? Why is the abyss if ocean not bridged with it. The answer is that coral only lives under certain limitations; it can only thrive at certain depths, in water of certain temperatures and salinities; outside these limits it languishes and dies. Science is like coral in this. Scientific investigators can only work in certain spots of the ocean of Being, where they are at home, and all outside is unknown to them...

Populations of bacteria live in the spumes of volcanic thermal vents on the ocean floor, multiplying in water above the boiling point. And far beneath Earth's surface, to a depth of 2 miles (3.2 km) or more, dwell the SLIMES (subsurface lithoautotrophic microbial ecosystems), unique assemblages of bacteria and fungi that occupy pores in the interlocking mineral grains of igneous rock and derive their energy from inorganic chemicals. The SLIMES are independent of the world above, so even if all of it were burned to a cinder, they would carry on and, given enough time, probably evolve new life-forms able to re-enter the world of air and sunlight.

Reality is never skin-deep. The true nature of the earth and its full wealth of hidden treasures cannot be argued from the visible rocks, the rocks upon which we live and out of which we make our living. The face of the earth, with its upstanding continents and depressed ocean-deeps, its vast ornament of plateau and mountain-chain, is molded by structure and process in hidden depths.

Returning now to the Malay Archipelago, we find that all the wide expanse of sea which divides Java, Sumatra, and Borneo from each other, and from Malacca and Siam, is so shallow that ships can anchor in any part of it, since it rarely exceeds forty fathoms in depth; and if we go as far as the line of a hundred fathoms, we shall include the Philippine Islands and Bali, east of Java. If, therefore, these islands have been separated from each other and the continent by subsidence of the intervening tracts of land, we should conclude that the separation has been comparatively recent, since the depth to which the land has subsided is so small. It is also to be remarked that the great chain of active volcanoes in Sumatra and Java furnishes us with a sufficient cause for such subsidence, since the enormous masses of matter they have thrown out would take away the foundations of the surrounding district; and this may be the true explanation of the often-noticed fact that volcanoes and volcanic chains are always near the sea. The subsidence they produce around them will, in time, make a sea, if one does not already exist.

See, thro' this air, this ocean, and this earth,All matter quick, and bursting into birth.Above, how high progressive life may go!Around, how wide! how deep extend below!Vast chain of being, which from God began,Natures ethereal, human, angel, man,Beast, bird, fish, insect! what no eye can see,No glass can reach! from Infinite to thee,From thee to Nothing—On superior pow'rsWere we to press, inferior might on ours:Or in the full creation leave a void,Where, one step broken, the great scale's destroy'd:From Nature's chain whatever link you strike,Tenth or ten thousandth, breaks the chain alike.

Significant inventions are not mere accidents. The erroneous view [that they are] is widely held, and it is one that the scientific and technical community, unfortunately, has done little to dispel. Happenstance usually plays a part, to be sure, but there is much more to invention than the popular notion of a bolt out of the blue. Knowledge in depth and in breadth are virtual prerequisites. Unless the mind is thoroughly charged beforehand, the proverbial spark of genius, if it should manifest itself, probably will find nothing to ignite.

Standing beside each other, we feasted our eyes. Above us the cerulean sky deepened to an inky black as the remnants of the atmosphere gave way to the depths of space. The mighty Himalaya were now a sparkling relief map spread out before us and garnished with a gleaming lattice work of swirling glaciers. Even Cho Oyu, Lhotse and Makalu, all 8,000-meter giants, were dwarfed. To the east and west, Kanchenjunga and Shishapangma, two more great sentinels of the Himalaya, stood crystal clear over 100 kilometers away. To the north were the burnished plains of Tibet, and to the south the majestic peaks and lush foothills of Nepal. We stood on the crown jewel of the earth, the curved horizon spinning endlessly around us.

Such is the character of mathematics in its profounder depths and in its higher and remoter zones that it is well nigh impossible to convey to one who has not devoted years to its exploration a just impression of the scope and magnitude of the existing body of the science. An imagination formed by other disciplines and accustomed to the interests of another field may scarcely receive suddenly an apocalyptic vision of that infinite interior world. But how amazing and how edifying were such a revelation, if it only could be made.

The dimmed outlines of phenomenal things all merge into one another unless we put on the focusing-glass of theory, and screw it up sometimes to one pitch of definition and sometimes to another, so as to see down into different depths through the great millstone of the world.

The external resistance may also be varied. For instance, let mercury or some other liquid form part of a voltaic circuit, then the more deeply the conducting wire is immersed in the mercury or other liquid the less resistance does the liquid offer to the passage of the current Hence the vibration of the conducting wire in mercury or other liquid included in the circuit occasions undulations in the current…

The interior parts of the earth and its internal depths are a region totally impervious to the eye of mortal man, and can least of all be approached by those ordinary paths of hypothesis adopted by naturalists and geologists. The region designed for the existence of man, and of every other creature endowed with organic life, as well as the sphere opened to the perception of man's senses, is confined to a limited space between the upper and lower parts of the earth, exceedingly small in proportion to the diameter, or even semi-diameter of the earth, and forming only the exterior surface, or outer skin, of the great body of the earth.

The losses of the natural world are our loss, their silence silences something within the human mind. Human language is lit with animal life: we play cats-cradle or have hare-brained ideas; we speak of badgering, or outfoxing someone; to squirrel something away and to ferret it out. … When our experience of the wild world shrinks, we no longer fathom the depths of our own words; language loses its lustre and vividness.

The nature of matter, or body considered in general, consists not in its being something which is hard or heavy or coloured, or which affects the senses in any way, but simply in its being something which is extended in length, breadth and depth.

The only solid piece of scientific truth about which I feel totally confident is that we are profoundly ignorant about nature. ... It is this sudden confrontation with the depth and scope of ignorance that represents the most significant contribution of twentieth-century science to the human intellect.

The only solid piece of scientific truth about which I feel totally confident is that we are profoundly ignorant about nature. Indeed, I regard this as the major discovery of the past hundred years of biology. It is, in its way, an illuminating piece of news. … It is this sudden confrontation with the depth and scope of ignorance that represents the most significant contribution of twentieth-century science to the human intellect.

The other book you may have heard of and perhaps read, but it is not one perusal which will enable any man to appreciate it. I have read it through five or six times, each time with increasing admiration. It will live as long as the ‘Principia’ of Newton. It shows that nature is, as I before remarked to you, a study that yields to none in grandeur and immensity. The cycles of astronomy or even the periods of geology will alone enable us to appreciate the vast depths of time we have to contemplate in the endeavour to understand the slow growth of life upon the earth. The most intricate effects of the law of gravitation, the mutual disturbances of all the bodies of the solar system, are simplicity itself compared with the intricate relations and complicated struggle which have determined what forms of life shall exist and in what proportions. Mr. Darwin has given the world a new science, and his name should, in my opinion, stand above that of every philosopher of ancient or modem times. The force of admiration can no further go!!!

The President shall then, through the Isthmian Canal Commission … cause to be excavated, constructed and completed, utilizing to that end, as far as practicable, the work heretofore done by the New Panama Canal Company, of France, and its predecessor company, a ship canal from the Caribbean Sea to the Pacific Ocean. Such canal shall he of sufficient capacity and depth as shall afford convenient passage for vessels of the largest tonnage and greatest draft now in use, and such as may reasonably be anticipated, and shall be supplied with all necessary locks and other appliances to meet the necessities of vessels passing through the same from ocean to ocean.

Written by John Coit Spooner in the first Spooner Act (also known as the Panama Canal Act (1902), Ch. 1302, 32 Stat. 481), 'An Act To provide for the construction of a canal connecting the waters of the Atlantic and Pacific oceans' (28 Jun 1902), Congressional Record, 57th Congress, Sess. 1, Chap. 1302, Sect. 3, 482. It was signed by President Roosevelt the next day.

The ‘Doctrine of Uniformity’ in Geology, as held by many of the most eminent of British Geologists, assumes that the earth’s surface and upper crust have been nearly as they are at present in temperature, and other physical qualities, during millions of millions of years. But the heat which we know, by observation, to be now conducted out of the earth yearly is so great, that if this action has been going on with any approach to uniformity for 20,000 million years, the amount of heat lost out of the earth would have been about as much as would heat, by 100 Cent., a quantity of ordinary surface rock of 100 times the earth’s bulk. This would be more than enough to melt a mass of surface rock equal in bulk to the whole earth. No hypothesis as to chemical action, internal fluidity, effects of pressure at great depth, or possible character of substances in the interior of the earth, possessing the smallest vestige of probability, can justify the supposition that the earth’s upper crust has remained nearly as it is, while from the whole, or from any part, of the earth, so great a quantity of heat has been lost.

Therefore, these [geotectonic] models cannot be expected to assume that the deeper parts of the earth’s crust were put together and built in a simpler way. The myth about the increasing simplicity with depth results from a general pre-scientific trend according to which the unknown or little known has to be considered simpler than the known. Many examples of this myth occur in the history of geology as, for instance, the development of views on the nature of the seafloor from the past to the present.

Those who have occasion to enter into the depths of what is oddly, if generously, called the literature of a scientific subject, alone know the difficulty of emerging with an unsoured disposition. The multitudinous facts presented by each corner of Nature form in large part the scientific man's burden to-day, and restrict him more and more, willy-nilly, to a narrower and narrower specialism. But that is not the whole of his burden. Much that he is forced to read consists of records of defective experiments, confused statement of results, wearisome description of detail, and unnecessarily protracted discussion of unnecessary hypotheses. The publication of such matter is a serious injury to the man of science; it absorbs the scanty funds of his libraries, and steals away his poor hours of leisure.

True science and true religion are twin sisters, and the separation of either from the other is sure to prove the death of both. Science prospers exactly in proportion as it is religious; and religion flourishes in exact proportion to the scientific depth and firmness of its basis.

As quoted from the close of a recent lecture by Huxley in 'What Knowledge is of Most Worth'. Lectures in Education, by Herbert Spencer, delivered at the Royal Institution (1855). In The Westminster Review (Jul 1859), 22. Collected in Essays on Education and Kindred Subjects (1911), 41.

Unless you make yourself equal to God, you cannot understand God: for the like is not intelligible save to the like. Make yourself grow to a greatness beyond measure, by a bound free yourself from the body; raise yourself above all time, become Eternity; then you will understand God. Believe that nothing is impossible for you, think yourself immortal and capable of understanding all, all arts, all sciences, the nature of every living being. Mount higher than the highest height; descend lower than the lowest depth. Draw into yourself all sensations of everything created, fire and water, dry and moist, imagining that you are everywhere, on earth, in the sea, in the sky, that you are not yet born, in the maternal womb, adolescent, old, dead, beyond death. If you embrace in your thought all things at once, times, places, substances, qualities, quantities, you may understand God.

Very few people, including authors willing to commit to paper, ever really read primary sources–certainly not in necessary depth and contemplation, and often not at all ... When writers close themselves off to the documents of scholarship, and then rely only on seeing or asking, they become conduits and sieves rather than thinkers. When, on the other hand, you study the great works of predecessors engaged in the same struggle, you enter a dialogue with human history and the rich variety of our own intellectual traditions. You insert yourself, and your own organizing powers, into this history–and you become an active agent, not merely a ‘reporter.’

We have no faculties for passing beyond ourselves, yet in ourselves are unfathomed depths, unexplored powers and relations which need fathoming and searching into. As Schopenhauer says, if we would understand nature our course must not only be horizontal, but perpendicular.

We have reached the end of our journey into the depths of matter. We have sought for firm ground and found none. The deeper we penetrate, the more restless becomes the universe…: all is rushing about and vibrating in a wild dance.

We love to discover in the cosmos the geometrical forms that exist in the depths of our consciousness. The exactitude of the proportions of our monuments and the precision of our machines express a fundamental character of our mind. Geometry does not exist in the earthly world. It has originated in ourselves. The methods of nature are never so precise as those of man. We do not find in the universe the clearness and accuracy of our thought. We attempt, therefore, to abstract from the complexity of phenomena some simple systems whose components bear to one another certain relations susceptible of being described mathematically.

Why are the bones of great fishes, and oysters and corals and various other shells and sea-snails, found on the high tops of mountains that border the sea, in the same way in which they are found in the depths of the sea?

Xenophanes of Kolophon ... believes that once the earth was mingled with the sea, but in the course of time it became freed from moisture; and his proofs are such as these: that shells are found in the midst of the land and among the mountains, that in the quarries of Syracuse the imprints of a fish and of seals had been found, and in Paros the imprint of an anchovy at some depth in the stone, and in Melite shallow impressions of all sorts of sea products. He says that these imprints were made when everything long ago was covered with mud, and then the imprint dried in the mud.

[Fritz Haber's] greatness lies in his scientific ideas and in the depth of his searching. The thought, the plan, and the process are more important to him than the completion. The creative process gives him more pleasure than the yield, the finished piece. Success is immaterial. “Doing it was wonderful.” His work is nearly always uneconomical, with the wastefulness of the rich.

[T]here are depths of thousands of miles which are hidden from our inquiry. The only tidings we have from those unfathomable regions are by means of volcanoes, those burning mountains that seem to discharge their materials from the lowest abysses of the earth.

… for it is very probable, that the motion of gravity worketh weakly, both far from the earth, and also within the earth: the former because the appetite of union of dense bodies with the earth, in respect of the distance, is more dull: the latter, because the body hath in part attained its nature when it is some depth in the earth.[Foreshadowing Newton's Universal Law of Gravitation (1687)]

… just as the astronomer, the physicist, the geologist, or other student of objective science looks about in the world of sense, so, not metaphorically speaking but literally, the mind of the mathematician goes forth in the universe of logic in quest of the things that are there; exploring the heights and depths for facts—ideas, classes, relationships, implications, and the rest; observing the minute and elusive with the powerful microscope of his Infinitesimal Analysis; observing the elusive and vast with the limitless telescope of his Calculus of the Infinite; making guesses regarding the order and internal harmony of the data observed and collocated; testing the hypotheses, not merely by the complete induction peculiar to mathematics, but, like his colleagues of the outer world, resorting also to experimental tests and incomplete induction; frequently finding it necessary, in view of unforeseen disclosures, to abandon one hopeful hypothesis or to transform it by retrenchment or by enlargement:—thus, in his own domain, matching, point for point, the processes, methods and experience familiar to the devotee of natural science.

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- Carl Sagan